Beamtime session: HC-6093 Data file name: Online_analysis_EuLSCO_26_1_B_big_CDW_25K_andor1.spec Sample: Eu_LSCO p=0.26 Polarization: LV Temperature: 25 K counting time of each spectrum: 1200 seconds resolution: 0.052 eV

Model description

The model is a sum of three Gaussian functions:

$$I(E) = I_{\text{elastic}}(E) + I_{\text{phonon}}(E) + I_{\text{magnon}}(E)$$

Individual Components

1. Elastic Peak (First Gaussian)

$$I_{\text{elastic}}(E) = A_1 \exp\left(-\frac{(E - x_{1})^2}{2\sigma_1^2}\right)$$

where $\sigma_1 = \frac{\text{FWHM}_1}{2\sqrt{2\ln(2)}}$

2. Phonon Peak (Second Gaussian)

$$I_{\text{phonon}}(E) = A_2 \exp\left(-\frac{(E - x_{2})^2}{2\sigma_2^2}\right)$$

where $\sigma_2 = \frac{\text{FWHM}_2}{2\sqrt{2\ln(2)}}$

3. Magnon Peak (Third Gaussian)

$$I_{\text{magnon}}(E) = A_3 \exp\left(-\frac{(E - x_{3})^2}{2\sigma_3^2}\right)$$

where $\sigma_3 = \frac{\text{FWHM}_3}{2\sqrt{2\ln(2)}}$

Below are the constraints for the parameters:

Model 2 description

The model is a sum of four Gaussian functions:

$$I(E) = I_{\text{elastic}}(E) + I_{\text{phonon1}}(E) + I_{\text{phonon2}}(E) + I_{\text{magnon}}(E)$$

Note: The elastic peak center is a free parameter constrained between -0.01 and +0.01 eV, with resolution fixed at 0.052 eV. The resolution (FWHM) for both phonon peaks is also fixed at 0.052 eV, while the magnon peak resolution remains a fitted parameter.

Below are the constraints for the parameters:

Model 3 description

The model is a sum of two Gaussian functions and one convolved DHO function:

$$I(E) = I_{\text{elastic}}(E) + I_{\text{phonon}}(E) + I_{\text{magnon}}(E)$$

3. Magnon Peak (Convolved DHO)

The magnon peak is modeled using a damped harmonic oscillator (DHO) function convolved with a Gaussian resolution function.

Below are the constraints for the parameters:

Model 4 description

The model is a sum of three Gaussian functions and one convolved DHO function:

$$I(E) = I_{\text{elastic}}(E) + I_{\text{phonon1}}(E) + I_{\text{phonon2}}(E) + I_{\text{magnon}}(E)$$

Note: The elastic peak center is a free parameter constrained between -0.01 and +0.01 eV, with resolution fixed at 0.052 eV. The resolution (FWHM) for both phonon peaks is also fixed at 0.052 eV. The DHO function is convolved with a Gaussian resolution function fixed at 0.052 eV.

Below are the constraints for the parameters: